Question

In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y. 

Answer 1

In the given figure, ∠BAD = 78°, ∠DCF = x° and ∠DEF = y°. Find the values of x and y.

We have to find the value of x and y.

Since ,ABCD   is a cyclic quadrilateral

So     `angle A + angle BCD = 180°`  (Opposite angle of a cyclic quadrilateral are supplementary)

` angle BCD = 180° - angle A `     ` ( ∠ A = 78°)`

`angle BCD = 180° - 78°` 

  `angle BCD = 102°`    ..… (1)

`angle BCD + angleDCF = 180°`

                      `DCF = 180° - angle BCD `

x = 180° − 102°
   = 78°

Now in cyclic quadrilateral DCFE
x + y = 180°    (Opposite angles of a cyclic quadrilateral are supplementary)
y = 180° − 78°
   = 102°

Hence, x = 78° and y = 102°